Communicating well is a critical component of being a successful research mathematician.
Papers that are easy to read find more readers, which means more citations, more recognition and more potential collaborators for the authors. Of course, well-written papers sail much more quickly and easily through the peer review process.
Beyond research papers, mathematicians write grant proposals. Some are directed at experts in their field, but many are written for a general mathematical or scientific audience, or sometimes deans or politicians more broadly. Well-written proposals, accurately aimed at the correct target audience, are much more likely to get funded.
Talks that are accessible to a wide audience expand the network of mathematicians who appreciate your work. Talks that folks in your field can understand nurture collaborations.
Likewise, every talk is a job talk. Prepare, know your audience, teach something. You never know who is listening who may later mention your name to a department looking to hire in your field.
Math professors, just like professionals in any sector, write annual reports for each of their funded projects, whether to the NSF, private foundations, or their own University. They also write annual progress reports to their chair or dean; these play a critical role in determining their salary for the following year.
A typical math professor writes tens of letters of recommendation each year: these letters are probably the most important part of the students’ applications.
Mathematicians who can write and speak well have a tremendous advantage in getting publications, speaking invitations, citations, grants, fellowships, salary raises and well-placed students. Investing in becoming a better writer and speaker is an investment in your career success.
Advice on Reading and Listening to Mathematics
UM Resources to improve your WritingTake advantage of the resources offered by Michigan’s Sweetland Center for Writing. This is a great place to get advice on improving your writing, and sometimes even get paid to get that help! For example, through Sweetland you can:
- Meet with a writing expert to go over a grant proposal, research paper, dissertation passage, or any writing for a class. They’re not mathematicians, but YES they can help with math writing (this has been tested)
- Take a class that helps you write a research paper or your dissertation
- Join a dissertation writing group. You can even get paid to be a group leader.
- Consider applying for the Sweetland Writing Institute, a summer fellowship for students in the final stages of dissertation writing. This can supply a stipend in the summer without teaching, so that you can complete your degree.
- Consider applying for to be a Sweetland Fellow; this will give you an opportunity to teach writing about math as a GSI in the English Department. Rachel Webb recently did this.
- Igor Pak’s article on mathematical writing
- Detailed advice on writing from Igor Pak
- The MAA’s general principles of mathematical communication
- The MAA’s compilation of advice on writing mathematics
- The Mathematics Students Resource compilation of advice on writing mathematics
- Advice on Giving Colloquium Talks, from John E. McCarthy
- Advice on Giving Talks, from Jordan Ellenberg
- Be considerate of your Audience, by Terry Tao
- Talks are not the same as papers, by Terry Tao
- Advice on getting the most out of talks, from Ravi Vakil
- The MAA has a compilation of advice on giving a math talk.
- The Mathematics Students Resource has more advice on giving math talks.
- The Mathematics Students Resource has worksheets for preparing talks on The Big Picture and The Finer Points, as well as a Talk Checklist Form
Advice on preparing job documents from the Mathematics Students Resource
Advice on writing grant applications from the Mathematics Students Resource
- Search MSC (Mathematics Subject Classification) codes. An MSC code (eg 14N35) identifies a narrow subfield of math.
- First find codes you are interested in. You can browse the complete index of MSC codes. Or, search MathSciNet for a particular paper that you are interested in and see what codes it is assigned (You can also use ZbMath though the codes will be different.)
- On MathSciNet, you can click directly on the code to see a list of all papers with this classification. Or, find multiple codes that you are interested in and search these from MathSciNet’s homepage (under “Search Terms” select “MSC Primary/Secondary”).
- Browse the arxiv. This is where mathematicians post their preprints. You can subscribe here to get daily emails listing the author/title/abstract of new papers in whatever subjects interest you.
- Search forwards/backwards citations with google scholar or MathSciNet
- Talk to people
- The MAA awards several prizes for outstanding mathematical exposition
- The AMS also maintains a prize for mathematical exposition
- The Best Writing on Mathematics is a yearly collection (since 2009) edited by Mircea Pitici.
- The MAA lists even more examples of excellent math writing
Get a group of friends to discuss your current writing projects or upcoming presentations. This is one of the best ways to improve your mathematical communication. (Here’s why.) (And more reasons from the MAA.)
Evelyn Lamb who has a mathematics blog for Scientific American blog
Erica Klarreich, a free-lance science writer with extensive contributions, for example, to Quanta Magazine.